%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : RNG038-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:35:14 PM UTC 2026
% Result : Unsatisfiable 5.81s 2.04s
% Output : Refutation 5.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 22 ( 10 unt; 0 def)
% Number of atoms : 44 ( 9 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 47 ( 25 ~; 22 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 47 ( 47 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : sum(additive_identity,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity1) ).
fof(f2,axiom,
! [X0] : sum(X0,additive_identity,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity2) ).
fof(f6,axiom,
! [X0] : sum(X0,additive_inverse(X0),additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
fof(f8,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ sum(X1,X3,X4)
| ~ sum(X0,X1,X2)
| ~ sum(X0,X4,X5)
| sum(X2,X3,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_addition2) ).
fof(f14,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ product(X5,X1,X6)
| ~ product(X3,X1,X4)
| ~ sum(X0,X3,X5)
| ~ product(X0,X1,X2)
| sum(X2,X4,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity3) ).
fof(f16,axiom,
! [X2,X3,X0,X1] :
( ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2)
| X2 = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',addition_is_well_defined) ).
fof(f18,axiom,
! [X0,X1] :
( X0 != additive_identity
| product(X0,h(X0,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',some_property) ).
fof(f19,plain,
! [X0,X1] :
( additive_identity != X0
| product(X0,h(X0,X1),X1) ),
inference(reorient_equations,[],[f18]) ).
fof(f23,negated_conjecture,
b != additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_b_is_additive_identity) ).
fof(f24,plain,
additive_identity != b,
inference(reorient_equations,[],[f23]) ).
fof(f25,plain,
! [X1] : product(additive_identity,h(additive_identity,X1),X1),
inference(equality_resolution,[],[f19]) ).
fof(f33,plain,
! [X0,X1] :
( ~ sum(X0,additive_inverse(X0),X1)
| additive_identity = X1 ),
inference(resolution,[],[f16,f6]) ).
fof(f49,plain,
! [X2,X3,X0,X1] :
( ~ sum(X0,additive_identity,X3)
| ~ sum(X0,X1,X2)
| sum(X2,additive_inverse(X1),X3) ),
inference(resolution,[],[f8,f6]) ).
fof(f70,plain,
! [X2,X3,X0,X1,X4] :
( ~ product(X3,h(additive_identity,X1),X4)
| ~ sum(X3,X0,additive_identity)
| ~ product(X0,h(additive_identity,X1),X2)
| sum(X4,X2,X1) ),
inference(resolution,[],[f14,f25]) ).
fof(f140,plain,
! [X2,X0,X1] :
( sum(X2,additive_inverse(X1),X0)
| ~ sum(X0,X1,X2) ),
inference(resolution,[],[f49,f2]) ).
fof(f200,plain,
! [X2,X0,X1] :
( ~ product(X0,h(additive_identity,X1),X2)
| ~ sum(additive_identity,X0,additive_identity)
| sum(X1,X2,X1) ),
inference(resolution,[],[f70,f25]) ).
fof(f299,plain,
! [X0,X1] :
( ~ sum(X0,X1,X1)
| additive_identity = X0 ),
inference(resolution,[],[f140,f33]) ).
fof(f451,plain,
! [X0] :
( ~ sum(additive_identity,additive_identity,additive_identity)
| sum(X0,X0,X0) ),
inference(resolution,[],[f200,f25]) ).
fof(f452,plain,
! [X0] : sum(X0,X0,X0),
inference(forward_subsumption_resolution,[],[f451,f1]) ).
fof(f460,plain,
! [X0] : additive_identity = X0,
inference(resolution,[],[f452,f299]) ).
fof(f584,plain,
additive_identity != additive_identity,
inference(superposition,[],[f24,f460]) ).
fof(f591,plain,
$false,
inference(trivial_inequality_removal,[],[f584]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : RNG038-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.10 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.22/0.45 % Computer : n020.cluster.edu
% 0.22/0.45 % Model : x86_64 x86_64
% 0.22/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.45 % Memory : 8046.5625MB
% 0.22/0.45 % OS : Linux 6.8.0-71-generic
% 0.22/0.46 % CPULimit : 300
% 0.22/0.46 % WCLimit : 300
% 0.22/0.46 % DateTime : Sun Sep 27 23:02:04 UTC 2026
% 0.22/0.46 % CPUTime :
% 0.22/0.46 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.52 Running first-order theorem proving
% 0.24/0.52 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.81/2.04 % (3870233)Input is clausal, will run a generic CNF schedule.
% 5.81/2.04 % (3870238)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3516280419:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 5.81/2.04 % (3870244)dis-21_1_sil=8000:lcm=predicate:random_seed=4058326137:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 5.81/2.04 % (3870240)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3037926540:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 5.81/2.04 % (3870239)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=384963103:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 5.81/2.04 % (3870241)lrs+10_1_sil=8000:sp=occurrence:random_seed=1279553793:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 5.81/2.04 % (3870242)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1267026558:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 5.81/2.04 % (3870241)First to succeed.
% 5.81/2.04 % (3870241)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3870233"
% 5.81/2.04 % (3870243)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2272655920:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 5.81/2.04 % (3870244)Instruction limit reached!
% 5.81/2.04 % (3870244)------------------------------
% 5.81/2.04 % (3870244)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.81/2.04 % (3870244)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.81/2.04 % (3870244)CaDiCaL version: 2.1.3
% 5.81/2.04 % (3870244)Termination reason: Instruction limit
% 5.81/2.04 % (3870244)Termination phase: Saturation
% 5.81/2.04 % (3870244)Time elapsed: 0.103 s
% 5.81/2.04 % (3870244)Peak memory usage: 88 MB
% 5.81/2.04 % (3870244)Instructions burned: 117 (million)
% 5.81/2.04 % (3870242)Instruction limit reached!
% 5.81/2.04 % (3870242)------------------------------
% 5.81/2.04 % (3870242)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.81/2.04 % (3870242)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.81/2.04 % (3870242)CaDiCaL version: 2.1.3
% 5.81/2.04 % (3870242)Termination reason: Instruction limit
% 5.81/2.04 % (3870242)Termination phase: Saturation
% 5.81/2.04 % (3870242)Time elapsed: 0.118 s
% 5.81/2.04 % (3870242)Peak memory usage: 88 MB
% 5.81/2.04 % (3870242)Instructions burned: 118 (million)
% 5.81/2.04 % (3870243)Instruction limit reached!
% 5.81/2.04 % (3870243)------------------------------
% 5.81/2.04 % (3870243)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.81/2.04 % (3870243)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.81/2.04 % (3870243)CaDiCaL version: 2.1.3
% 5.81/2.04 % (3870243)Termination reason: Instruction limit
% 5.81/2.04 % (3870243)Termination phase: Saturation
% 5.81/2.04 % (3870243)Time elapsed: 0.102 s
% 5.81/2.04 % (3870243)Peak memory usage: 89 MB
% 5.81/2.04 % (3870243)Instructions burned: 181 (million)
% 5.81/2.04 % (3870254)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=2275897044:st=4:i=219:sd=3:ss=axioms_2995 on theBenchmark for (2995ds/219Mi)
% 5.81/2.04 % (3870253)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=672654837:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2996 on theBenchmark for (2996ds/189Mi)
% 5.81/2.04 % (3870252)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=1478492581:i=143:sd=2:aac=none:ss=axioms:sgt=16_2996 on theBenchmark for (2996ds/143Mi)
% 5.81/2.04 % (3870252)Also succeeded, but the first one will report.
% 5.81/2.04 % (3870241)Refutation found. Thanks to Tanya!
% 5.81/2.04 % SZS status Unsatisfiable for theBenchmark
% 5.81/2.04 % SZS output start Proof for theBenchmark
% See solution above
% 5.81/2.04 % (3870241)------------------------------
% 5.81/2.04 % (3870241)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.81/2.04 % (3870241)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.81/2.04 % (3870241)CaDiCaL version: 2.1.3
% 5.81/2.04 % (3870241)Termination reason: Refutation
% 5.81/2.04 % (3870241)Time elapsed: 0.023 s
% 5.81/2.04 % (3870241)Peak memory usage: 88 MB
% 5.81/2.04 % (3870241)Instructions burned: 19 (million)
% 5.81/2.04 % (3870241)------------------------------
% 5.81/2.04 % (3870241)------------------------------
% 5.81/2.04 % (3870233)Success in time 0.725 s
% 5.81/2.04 % Vampire exiting
%------------------------------------------------------------------------------